I done good  

mosaic tile table japan
I have seen mosaic tables like your tile table with that type of leg, plywood backing, and the black tile w/ white grout edging that had a Made in Japan stamp on them and one even had a manufacturer name (but I have forgotten what it was). Pink, black and white seem to be a popular color for the tiles from the small sampling I've seen; usually low coffee tables or end tables. I tried to scare up a picture from my phone, but I must have deleted it. If I find one. I'll post.
EDIT: Nevco is the maker/importer mark I saw with the Japan stamp. I found the pictures.

One-off custom-made
furniture, unmarked, will be impossible to assign to a maker, absent provenance or some accidental discovery. One might look into the early career of Dakota Jackson, who apparently started as a stage magician, then migrated into custom desks with secret compartments, leading to a career in art furniture and eventually to production high-end furnishings.
But this piece is so clearly a display case, perhaps for a boutique jeweler. Its form is entirely a result of whim -- either on the part of the client or the maker. It doesn't have to mean anything more than that -- delightful and strange though it be. An amazing find.
Does the silver-colored button (?) on the edge have a function ? A light switch, perhaps ?
The pattern of tiles on the table is reminiscent of age-old handcraft of many kinds, including ceramic decoration and rug-weaving. Skilled and practiced hands might produce such effects with amazing speed . . .

The silver button on the side...
The silver button on the side/ edge is a lock that locks the case shut from the bottom. It still has the original key and actually works. Anyone who wanted to steal the contents could just as easily break the glass rather then open the bottom hinge.
I agree it's likely a one off or custom piece made to fit the user. The butcher block seems to be held together by some 1/2" or so lags but I can't tell if they go all the way through and they are quite rusty.. I'm glad to know you also find it unique. The only reason I don't think it was a display case for a retail setting is because the glass part is not very big, or secure. that's what makes me think it's a vanity. I'll keep scouring for marks later today.
As for the table (not sure if it's tile or what) , could be homemade, japan etc. I'm more curious about the desk at this point.
The chairs are incredibly comfortable even without the upholstery. The backrests are at the perfect height for someone 6"2.

There are a few points about ...
There are a few points about the desk that I am seeing:
1. it would be nearly impossible to arrange jewelry in it. Imagine, you swing down the bottom, sit on the floor and then what, pin the jewelry into place with it flopping everywhere? Complicated. I think whatever was displayed in there had to have been pinned into place, but it also had to be rigid enough to make that easy. And then to extract said item: complicated. I think this suggests _against_ it as a vanity. I think it does suggest the items inside the display were semi-permanent sales displays.
2. the light is aimed at the person behind the desk (lock side), so the displayed objects would not have looked very good to said person. But the light would bounce off nicely for someone in front of the desk. Perhaps a passing customer. Again, this suggest _against_ it as a vanity, and towards a sales display.
3. The large open space on the left would be useful for a tall display or perhaps a cash box.

Some Interesting points. The...
Some Interesting points. The more I look at it, the more I have to agree that it's original purpose was as a display case, I just cAnt think of what would be displayed in such a shallow case other than jewlery. Documents or credentials? Good point about the cash box. Underneath on the left there are screw holes that may resemble where a drawer once was.
I think it dates to the 40s or earlier because of the patina, wiring and rusty lags that are visible behind the light. Some bits have been replaced, hinges and screws etc. maybe a case for brooches haha?
Any comments on design or era? Or do you think the shape serves a specific purpose?
Thanks for all the help guys n gals.

.
ps (at the top) of course you know that I'm only typing like a fool, I like your odd desk.
If I were to put anything in it, I'd like to see an artfully positioned combination of the following items.
~a tooth ( human or whatever)
~a bicycle sprocket
~a small photo of Agnus Moorehead
~faux slices of bacon (cooked)
~a receipt from Good Vibrations
~and an unopened letter.
Best,
Aunt Mark

Aunt Mark,
I used to have a cow tooth but I haven't seen it in awhile. The enamel was very worn.
Tex, mosaic tile like that came in square foot sections, glued to a mesh backing and arranged so that each sheet interlocked. It's still made that way.

Tex,
your funny little desk makes me think it's an amateur magician's prop..a little slight of hand razzmatazz to delight and upset children of all ages...
I remember seeing that same mosaic coffee table in a thrift store about a year ago, no markings also. Thought it was homemade, like a build your own coffee table kit...also maybe to delight and upset children of all ages 😉

No need to patronize my...
No need to patronize my desk!?!?

.
Actually Tex, I thought it was an interesting quirky table...and though display case seemed the most reasonable, I couldn't help but think magician's table, or a table for some other completely out there purpose..which would be pretty interesting too...no offense intended 🙂

Gotcha hah. I wasn't sure, an...
Gotcha hah. I wasn't sure, and I was trying way to hard to put patronize and this desk in the same sentence.
It's natural habitat.

Hi *spanky*.
So sorry to hear of the misplaced tooth. I used to have a small framed picture of Agnus Moorehead next to my bed during my first childhood years... that I've temporarily misplaced.
Oh,
Aunt Mark